AbstractThe analysis of resonant electrical length and unloadedQfor the miniaturized dielectric coaxial stepped impedance resonator (SIR), used often in diplexers of portable radio telephones, is performed usually with the assumption of only fundamental TEM mode.In this paper, finite element TM mode analysis is performed and optimum structure design of SIR is shown which makes the ratio of unloadedQto the resonant electrical lengthkL(Q/kL) maximum. As a result of analysis, it is found that the location of the step to minimize resonant electrical length is about 40 percent of the axial length from the open end of SIR.The ratio of unloadedQand resonant electrical length varies rather slowly when any of the structure parameters are varied around the optimum value. This fact shows that no high precision in the design of structure parameters is required. Moreover, providing taper at the step position in SIR, the resonant electrical length can be increased by a few percent.It is shown also that the present analysis is useful for the design of square‐shaped SIR which is a simple and practically used structure for diplexer